In the hours after Tuesday’s surprise announcement that Citigroup chief executive Vikram Pandit was stepping down, speculation was rife, and facts scant, about what is ahead for the nation’s third-largest bank.

Pandit left after a series of embarrassments and missteps that apparently unsettled Citigroup’s board, including a ‘‘no’’ vote from shareholders on his pay package and a ruling from the Federal Reserve that the bank was not strong enough to raise its stock dividend.

Under his successor, one possibility given high odds by financial analysts is a strategy of more cost-cutting, more shrinking, and more focus on boring, traditional banking, such as making loans.

‘‘It’s going to get a lot smaller,’’ said Gerard Cassidy, a longtime banking analyst at RBC Capital Markets. ‘‘You’ve got to shrink to make big money.’’

In the nearly five years since Pandit became chief executive, he shed businesses and slashed jobs. Staff fell from 375,000 when he took control to 262,000.

Once the nation’s largest bank, Citi is now the third-largest, with $1.9 trillion in assets. It trails JPMorgan Chase, with $2.3 trillion, and Bank of America, with $2.1 trillion.

Citi’s new chief executive is Michael Corbat, 52. He had been chief executive of Citigroup’s Europe, Middle East, and Africa division. He also ran Citi Holdings, with assets Citi wants to sell.

Because Corbat is not widely known, analysts Tuesday were not sure how he might change the company’s direction.

For clues, some look to someone more well-known: the man thought to be behind Pandit’s departure, Citi chairman Michael O’Neill. He became chairman in March, when Richard Parsons left.

O’Neill was elected chief executive of Barclays, the British bank, in 1999 but had to give up the job immediately because of heart problems. He joined Citi’s board in 2009. O’Neill had also been chief executive of Bank of Hawaii Corp., where he was a big cost-cutter.

‘‘When he ran Bank of Hawaii, he shut down up to 50 percent of its branches. It’s a startling number,’’ said Cassidy. He added that at Citi, ‘‘if the branch banking businesses doesn’t make sense in parts of the United States, [he’ll] get rid of it.’’

Tom Brown, founder of hedge fund Second Curve Capital, agreed.

‘‘O’Neill downsized tremendously, and that’s what I think you’ll see here,’’ he said.